The only thing I would say about your RT call is that it's fine, but don't worry about the ATIS unless you're inbound to that particular airfield. The controller concerned will put you on the pressure he wants you on if you're just a transit.
As for stating the type of service required on the initial call it's nice as it helps you prioritise, as well as deciding whether to issue a squawk or not.
Funny you should mention about the strips. The different types are not used for type of service, but whether the flight is inbound or just a transit. Letting us know whether a flight is inbound or just an area transit early on in the proceedings (especially if you haven't booked in) is a great help.
CM